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貝氏變數與稀疏群結構選取方法 = Bayesian Approaches...

國立高雄大學統計學研究所博士班

貝氏變數與稀疏群結構選取方法 = Bayesian Approaches for Variable Selection and Sparse Group Selection

紀錄類型:	書目-語言資料,印刷品 : 單行本
並列題名:	Bayesian Approaches for Variable Selection and Sparse Group Selection
作者:	朱基祥,
其他團體作者:	國立高雄大學
出版地:	[高雄市]
出版者:	撰者;
出版年:	民104[2015]
面頁冊數:	70面圖,表 : 30公分;
標題:	貝氏變數選取
標題:	Bayesian variable selection
電子資源:	http://ethesys.nuk.edu.tw/ETD-db/ETD-search-c/view_etd?URN=etd-0210115-111606
附註:	105年3月31日公開
附註:	參考書目：面66-70
摘要註:	這篇論文提供了在迴歸模型下，針對具有貝氏結構之解釋變數選取與疏群結構選取的方法。在變數選取方面，我們推廣陳等人(2011)提出的兩個演算法至異質性的模型，並且修改隨機匹配追蹤演算法，利用將解釋變數分段匹配的方式，提高演算法的效率。而對於解釋變數具有群結構的問題上，著重於解釋變數分別被分到數個不相交的群的情況。類似群體選取方法中的稀疏性假設，我們考慮只有少數的重要群體對反應變數具有解釋力。然而，在稀疏群結構選取方法中，也考慮對反應變數具有影響力的群體中的稀疏性，也就是，假設在每個有影響力的群體中，只有少數解釋變數會影響反應變數的變化。在這個問題上，我們採取貝氏分層結構的方式，在每個群體給予一個指示函數，來表示該群體是否對反應變數具有影響力。而在每一個群體中的每一個解釋變數，我們也賦予一個指示函數，來表示該解釋變數是否對反應變數具有影響力。在此貝氏結構下，稀疏群結構選取方法可藉由兩層結構的後驗分佈，來決定那些對反應變數具有影響的群體及變數，並得到其影響係數。這裡我們採取群結構吉布斯抽樣演算法來得到後驗分佈的樣本點。藉由模擬結果，群結構吉布斯抽樣演算法在對於具有影響反應變數的群體中，在選取真正對反應變數有影響的解釋變數選取方面上，比稀疏群結構的Lasso方法有較好的選取結果。 This thesis considers the Bayesian framework for the variable selection and focuses on the sparse group selection problems in the regression model. In the variable selection problem, we first extend the algorithm in Chen et al. (2011) for heteroscedastic regression model and modify stochastic matching pursuit algorithm to be more efficient via blocked window moving approach, especially when the number of variables is large. For the grouped variables problem, the variables (or regressors) are partitioned into different distinct groups. Similar to the sparsity of group selection approach, we assume that only small number of groups are active or important to explain the response variable. However, we also consider the sparsity of active groups, that is, there are few active variables in each active group. We adopt a Bayesian hierarchical formulation, such that each candidate group is associated with a binary variable to indicate whether the group is active or not. Within each group, each candidate variable is also associated with another binary indicator to denote that the variable is active or not. In this Bayesian formulation, the sparse group selection problem can be solved by sampling from the posterior distribution of the two layers of indicator variables as well as the coefficients of the selected variables. We adopt a group-wise Gibbs sampler for posterior sampling and demonstrate the proposed method by simulation studies as well as real examples. The simulation results show that the proposed method performs better than the sparse group Lasso in terms of selecting the active groups and identifying the active variables within the selected groups.

貝氏變數與稀疏群結構選取方法 = Bayesian Approaches for Variable Selection and Sparse Group Selection
朱, 基祥

貝氏變數與稀疏群結構選取方法 = Bayesian Approaches for Variable Selection and Sparse Group Selection / 朱基祥撰 - [高雄市] : 撰者, 民104[2015]. - 70面 ; 圖,表 ; 30公分.
105年3月31日公開參考書目：面66-70.
貝氏變數選取Bayesian variable selection

貝氏變數與稀疏群結構選取方法 = Bayesian Approaches for Variable Selection and Sparse Group Selection
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